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This question already has an answer here:

The government is a totalitarian oligarchy, and is relatively new. There is no organized opposition yet. The government is pretty well organized. It is extremely popular among the 80% of the population (cult of personality level popular), and 20% of the population dislike it but are terrified and docile at the moment.

They have modern technology, so manufacturing is somewhat automated and farming is heavily automated. They have access to modern high yield crop cultivars, GMOs, fertilizers, and modern pesticides. Their medicine is modern. Infrastructure is well developed, the population is educated and vaccinated. The population is used to deprivation and hardship, and can survive on the bare essentials without unrest. They do not require entertainment, eat extremely bland food, work long hours for seven days a week without complaint, and live mainly in shacks and tiny apartments in prefabricated concrete high rises, so that almost all resources can be devoted to capital and military goods.

They are in a state of total war against an existential threat, so people are clinging to the government desperately, even the ones that hate it, as they do not want to die. How large of a military (including combat forces and logistics people) can be mobilized for at least 5 years, without causing mass starvation? Even the dissidents can be mobilized, as they will find it difficult to make trouble if led by loyal NCOs and officers and controlled by secret policemen.

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marked as duplicate by cobaltduck, Anketam, Mark Olson, Tim B II, JBH May 30 '18 at 23:23

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    $\begingroup$ For the reference, North Korea has about 1 million strong army for about 25 million population. $\endgroup$ – Alexander May 30 '18 at 19:54
  • $\begingroup$ Welcome to WorldBuilding, Richard Smith! If you have a moment please take the tour and visit the help center to learn more about the site. You may also find Worldbuilding Meta and The Sandbox (both of which require 5 rep to post on) useful. Have fun! $\endgroup$ – FoxElemental May 30 '18 at 19:58
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    $\begingroup$ The magic number seems to be 6%. It's roughly what countries were able to field in WWII. $\endgroup$ – user47242 May 30 '18 at 20:04
  • $\begingroup$ Have a look at Switzerland with some 80'000 people in active Service and another ~80'000 that could be called up, at a population of some ~8mio people (The army has been downsized in recent years) $\endgroup$ – dot_Sp0T May 30 '18 at 20:44
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In the immortal words of James Carville... "It's the economy, stupid!"

Population is not the primary determining factor for military size. Your economy is. Your military must be equipped, fed, housed, trained, transported, and above all, paid. Humans are relatively cheap compared to everything else.

The United States (pop 300,000,000) spends 54% of its discretionary budget or 22% of the whole on its standing military of 1.28 million.

  • Ratio of population to military: ~234:1 (0.4%)
  • Ratio of tax revenue to military spending: 22% (726 Billion)
  • Cost of each soldier: $567,000. * Economic (tax) value of each citizen: $2,420

Here's my point, one out of every 234 people is itsy-bitsy. During WWII 12% of our population served. Compared to today, that would be a standing army of 36 million. Could we sustain that?

Heck, no!

Because we're already spending 22% of our taxes on our military. Granted, it gets more efficient when most of your draftees are handed the most basic of equipment (gun, helmet, MRE, change of underwear...), but I very much doubt the U.S. economy could withstand a 36 million man army (at least not without debilitating taxes and even then not for very long).

So, in the end, it's not your population that dictates the size of your military, it's your economy. If The U.S. population was twice what it is (600M) and the average income was half what it is, the end result would be an army the size it is today. It's all we could afford.

Conclusion

If your 10M population is no more productive than the average U.S. citizen, then the largest your military can be is (2,420 * 10,000,000)/567,000 = 42,680 or 43K troops maintained at current U.S. standards.

Whis is a long way of saying, 300M/1.29M = 10M/X

More to the point, how much you can stand depends on how wealthy you make your people, and that's an issue for your story. If they're poor, the army will be small. If it's more, it will be larger. If they invest in technology over people, it will be smaller. If they invest in people over technology, it will be larger.

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    $\begingroup$ You are making a wrong correlation here. You are basing the size on America's economy and assume all countries will have the exact same spending per soldier. North Korea has 28.5billion total to spend on its country and far less dollars per soldier spend. If the OP's country knew of its crisis beforehand its likely like soviet countries or other countries that fear invasion has old wargear locked away for paramilitaries to use once war breaks out. Better an old tank than no tank at all. $\endgroup$ – Demigan May 30 '18 at 21:20
  • $\begingroup$ I'm generally anti-military but these numbers don't look correct. You have to correlate the cost per soldier in personal care and standard effects. One tomahawk missile costs more than the operational lifetime of something like 500 soldiers (no sources to back that but it's a calculation of 50k / year @4 year service based on 100m cost of missile) - or in short, equipment cost is factored differently. If your army had nothing but horses and swords your correlation would sound more accurate. $\endgroup$ – Kai Qing May 30 '18 at 21:30
  • $\begingroup$ @Demigan, I took the OP at his word. "They have modern technology, so manufacturing is somewhat automated and farming is heavily automated. They have access to modern high yield crop cultivars, GMOs, fertilizers, and modern pesticides. Their medicine is modern. Infrastructure is well developed, the population is educated and vaccinated." He didn't describe a population suffering hardship, such as the North Koreans, only that they could. ALL countries, knowing of the crisis beforehand, can increase their military, but the OP asked for a "sustainable" size. This is my opinion. $\endgroup$ – JBH May 30 '18 at 21:37
  • $\begingroup$ @KaiQing, The OP said he had a modern society with modern technology. That doesn't sound third-world to me. It sounds like horses and swords to you when I'm sourcing numbers from 2017-2018 US military statistics? I'll take my sourced numbers over your guesswork any day of the week. If you don't think I'm correct, you're invited to write your own answer. That would be in the OP's best interest anyway. $\endgroup$ – JBH May 30 '18 at 21:41
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    $\begingroup$ The United States of America does not spend 54% of its budget on its armed forces. It spends 54% of its discretionary budget on its armerd forces. The discretionary part of the the budget is about 40% of the total budget; it is of this 40% that the armed forces take 54%, which means that the part spent on the military is about 22% of the total. Which is still an very large part, but nevertheless much less insane then 54% would be. $\endgroup$ – AlexP May 30 '18 at 22:36
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North Korea, which has 5.8% of its census population (including children and elderly people incapable of serving in the military) is the most militarized society on Earth and approaches the practical limits of mobilization in the circumstances that you describe. Indeed, they are right at the brink of the standard you describe because they have experienced mass starvation costing millions of lives as a result of their guns v. butter decisions, but have nonetheless proved capable of sustaining their military mobilization.

Thus, for a country with 10 million people, the largest possible sustainable military would be about 600,000 troops.

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  • $\begingroup$ Actually, NK has perhaps 7,679,000 soldiers, counting active military, reserves, and paramilitary, which is 30% off their population, although many of those are used as work crews and not combat personnel. But I am talking about a technologically advanced society and not a backwards one like North Korea. Their technology is around US levels, their factories are automated, so few manual labors are needed there, and less than 3% of the population is needed for farming and food processing. $\endgroup$ – Richard Smith May 30 '18 at 20:09
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    $\begingroup$ @RichardSmith By any consistent definition you choose NK is going to be close to the limit, and I don't think you could establish or sustain a regime like that in a place with technology around US levels. US technology and economic efficiency is directly a product of not having the kind of regime that you describe. $\endgroup$ – ohwilleke May 30 '18 at 20:29
  • $\begingroup$ The USSR would also be similar to this state, and it was much better run. While there were shortages of consumer goods and most foods, starvations was rare after WWII, as there was generally enough bread, cabbage, and vodka. Even with a weak economy, the USSR had a large military with technology equal to or superior to US technology, especially in the fields of artillery, missiles, and tanks. Even with the lack of incentives, inefficiencies caused by central planning, and lack of market signals, the USSR's GDP was still #2 for most of its existence and it was pretty good at heavy industry. $\endgroup$ – Richard Smith May 30 '18 at 22:58

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